Conditions under which it is possible to design a correct algorithm and a six-level spatial neural network reproducing the computations performed by this algorithm for recognition problems with binary data (-regular p...
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Conditions under which it is possible to design a correct algorithm and a six-level spatial neural network reproducing the computations performed by this algorithm for recognition problems with binary data (-regular problems) are found. A distinctive feature of this network is the use of diagonal activation functions in its internal layers, which significantly simplify intermediate computations in the inner and outer loops. Given an -regular problem, the network sequentially computes the rows of the classification matrix for the test sample objects. The computational process (i.e., the inner loop) for each test object consists inside the elementary 3-level network (i.e., -block) of a single iteration determined by a single object of the training set. The proposed approach to the neural network construction does not rely on the conventional approach based on the minimization of a functional;rather, it is based on the operator theory developed by Zhuravlev for solving recognition and classification problems.
Algebra over estimation algorithms with addition, multiplication by a constant, and normalization operations is investigated. Normalization is interpreted as a linear (with respect to each row) transformation of the m...
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Algebra over estimation algorithms with addition, multiplication by a constant, and normalization operations is investigated. Normalization is interpreted as a linear (with respect to each row) transformation of the matrix of estimates that takes the maximum entry of the row to unity and the minimum entry to zero. The algebraic closure is described, a formula for its dimension is obtained, and correctness criteria are formulated.
It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model o...
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It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained.
An algebra over recognition algorithms supplemented with a normalization operation (under various definitions) and the division operation is investigated. correctness criteria for various algebraic closures are obtain...
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